Weight shiftings for automorphic forms on definite quaternion algebras, and Grothendieck ring

摘要

Let p be a prime number and let F be a finite field of characteristic p. We investigate the interplay between the algebraic structure of the Grothendieck ring of finitely generated F[GL(2)(F)]-modules, and the existence of cohomological operators producing congruences modulo p between automorphic forms on definite quaternion algebras over a totally real field.